Answer:
14014
Step-by-step explanation:
base of stone pyramid=154
height=91
b×h
154×91=4014
Write the phrase as an expression.
a number t cubed
Answer:
[tex]t^{3}[/tex]
Step-by-step explanation:
cubed means to the power of 3
How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)
Answer:
Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].
[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].
[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].
Step-by-step explanation:
Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].
Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].
Since [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:
[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].
integral from 0 to 5 of x^2 + 3 dx
Answer:
=170/3 or (decimal 56.67)
Step-by-step explanation:
Steps
∫⁵ x²+3dx
⁰
Apply the Sum Rule: ∫fx) + gx) dx = ∫f(x)dx +-∫ g(x)
dx
∫⁵ x² dx +∫⁵ 3dx
⁰ ⁰
∫⁵ x² dx=125/3
⁰
∫⁵ 3dx=15
⁰
125/3+15
=170/3
Suppose a cylinder that holds 3 L of liquid must be created. Determine the radius and height of the cylinder that will minimize the amount of material used in its construction.(Note: 1 L=1,000 cm^3)
The radius and the height of the dimension that will minimize the amount of material used in the construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.
How to find the dimension that minimizes a cylinder?The dimension that minimizes the surface area of a cylinder can be determined by:
Drawing the picture of the problem, Write down & identify optimization as well as the constraint equations;Use the derivative of the optimization equation to find the dimensions.Given that:
1 L = 1000 cm³3 L = 3000 cm³The area of the cylinder = (2 πr)h + 2(πr²)
A = 2πrh + 2πr²The volume of the cylinder
V = πr²hLet's identify the constraint equation and Optimization equation:
To minimize the surface area of the can, we have:
Area equation = Optimization equationThe constraint equation is the equation that limits us:
Volume equation = constraint equationSo, Let's solve for h in our volume equation, we have:
3000 = πr² h
h = 3000/πr²
Now, from the Area equation
[tex]\mathbf{A = 2 \pi r(\dfrac{3000}{\pi r^2}) + 2\pi r^2}[/tex]
Taking the derivate and setting it to zero, we have;
Derivative:
[tex]\mathbf{A = \dfrac{6000}{ r}+ 2\pi r^2}[/tex]
[tex]\mathbf{A = 6000 r^{-1} + 2\pi r^2}[/tex]
[tex]\mathbf{A' = -6000 r^{-2} + 4\pi r}[/tex]
[tex]\mathbf{A' = 4\pi r-\dfrac{6000}{ r^{2} }}[/tex]
Setting it to zero, we have:
[tex]\mathbf{0=\dfrac{ 4 \pi r^3 - 6000}{r^2}}[/tex]
Factor out 4
0 = 4(πr³ - 1500)
1500 = πr³
r³ = 1500/π
[tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex]
The above is the radius that minimizes the surface area of the cylinder;
From [tex]\mathbf{h = \dfrac{3000}{\pi r^2}}[/tex]
[tex]\mathbf{h = \dfrac{3000}{\pi ( \sqrt[3]{\dfrac{1500}{\pi}} )^2}}[/tex]
[tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex]
Thus, the radius and height that minimize the amount of material to be used in its construction are [tex]\mathbf{r = \sqrt[3]{\dfrac{1500}{\pi}} }[/tex] and [tex]\mathbf{h = \dfrac{3000}{\pi ({\dfrac{1500}{\pi}} )^{2/3}}}[/tex] respectively.
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Type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5% every year. if at the start of the year the population is at 10,000 beetles, what will its population be after three years? at the end of the third year the population of beetles will be .
At the end of the third year the population of beetles will be 11,576beetles
Exponential equationsThe standard form of an exponential function is given as:
y = ab^t
Given the following parameters
initial population 'a" = 10,000 beetles
Time = 3 years
rate b = 1.05
Substitute into the formula
y = 10,000(1.05)^3
y = 10,000(1.1576)
y = 11,576 beetles
Hence at the end of the third year the population of beetles will be 11,576beetles
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Please help me with this math problem!! I will give brainliest!! :)
Wrong answer sorry. Hope you find it!
What is the remainder of (x3+5x2−32x−7)÷(x−4) ? Enter your answer in the box.
Answer:
x^2+5x-36-7/x
Step-by-step explanation:
assuming x^3 and 5x^2
(100 points + brainliest)
A box of chocolates contains five milk chocolates, three dark chocolates, and 8 white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate.
What is the probability that this event happens? Show all of your steps used to solve this problem.
Answer:
3.6%
Step-by-step explanation:
This is an example of dependent events. When events are dependent, you have to multiply the probability of each event that happens after each other. Probability is desired outcome over all possible outcomes. For the milk chocolate, there are 5 pieces we can pick out of 16, so it's 5/16. Next, the probability of dark chocolate is 3/15 (There is one less piece of chocolate overall now). For the white chocolate, the possibility is 8/14. So now we have to multiply:
5*3*8 120 1
______ = _____ = ___ = (about) 0.036
16*15*14 3360 28
So, that's 3.6%
Hope this helps!
What is the height of a cylinder if the diagonal is 13 inches and the radius is 5 inches?
Answer:
12 inches.
Step-by-step explanation:
You have to use the pythagorean formula. The measurements you stated form a right angle. Therefore, a^2 + b^2 = c^2. In this equation, we know c=13, and b=5. So therefore c^2 - b^2 = 144. We have to solve for a, so square root 144 to get 12.
Answer:12 in
Step-by-step explanation:
Which of the following are roots of the polynomial function? Check all that apply. F(x) = x3 - 5x2 - 13x - 7
Answer:
Write properties of function:
x intercept/zero: [tex]x_{1} =-1;x_{2} =7[/tex]
Step-by-step explanation:
x² - 6x - 7 = x² - 7x + x - 7
⇒ x(x - 7) + 1(x - 7)
⇒ (x + 1) (x - 7)
Thus, x³ - 5x² - 13x - 7 = (x + 1)(x + 1)(x - 7)
[tex]~~~~~~~~x^3 -5x^2 -13x -7=0\\\\\implies x^3 +x^2 -6x^2 -6x-7x-7=0\\\\\implies x^2(x+1) -6x(x+1) -7(x+1)=0\\\\\implies (x+1)(x^2 -6x -7) = 0\\\\\implies (x+1)(x^2 +x -7x-7)=0\\\\\implies (x+1) [x(x+1) -7(x+1)]=0\\\\\implies (x+1)(x+1)(x-7) = 0\\\\\implies (x+1)^2 (x-7) = 0\\\\\implies x = -1,~ x = 7\\\\\text{Hence, the roots are}~ -1~ \text{and}~ 7[/tex]
PLEASE HELP ME!!
find the Trinomial!
Answer:
[tex]a^{4}-2a^{2} -24[/tex]
Step-by-step explanation:
We do FOIL to solve this
Equation of a line that goes through the following points: (4,1) and (7,10)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11[/tex]
You decide to buy a tablet for college. The tablet you want is currently on sale for 29% off the original price. If the original price was $899, what is the current price? Round your answer to the nearest cent (2 decimal places).
Answer:
638.29
Step-by-step explanation:
This is the answer because 29 percent of 899 is somewhere around 260.71
Substract that and you get 638.29
pleae awnser :))) hhoh
Answer:
the answer will be
K' = -9, 5
L' = 0,5
M' = -8,3
Step-by-step explanation:
the x axis is written first and the y axis is written after that.
hope it helps!!
PLEASE MARK BRAINLIEST !!..
Answer:
K': (9,5)
L': (0,5)
M': (8,3)
Step-by-step explanation:
Tell me if im wrong!
Passengers, who are travelling in a car west along a road that runs east-west, see a mountain 9 km away on a bearing of 290°. When they have travelled a further 5 km west along the road, what will be the distance to the mountain?
A sequence is defined recursively by the formula f(n 1) = –2f(n). the first term of the sequence is –1.5. what is the next term in the sequence? –3.5 –3 0.5 3
Given that the first term of the sequence is –1.5, the next term of the sequence would be 3
How to determine the next term?The recursive function is given as:
f(n + 1) = -2f(n)
Substitute 1 for n
f(1 + 1) = -2f(1)
Evaluate
f(2) = -2f(1)
Given that the first term is -1.5, the equation becomes
f(2) = -2 * -1.5
Evaluate
f(2) = 3
Hence, the next term of the sequence is 3
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Answer:
(D) 3
Step-by-step explanation:
Amina and her mother are buying green coffee beans to make qahwa, an Arabic
coffee recipe. Green coffee beans cost $0.58 for each ounce. Amina and her
mother buy 12.5 ounces of green coffee beans. What is the total cost of the green
coffee beans?
Answer:
$36.3
Step-by-step explanation:
The total cost of the Green coffee beans is $7.25.
What is Total Cost?Total cost (TC) is the minimum cost of producing some quantity of output. This is the total economic cost of production and is made up of variable cost, which varies according to the quantity of a good produced and includes inputs such as labor and raw materials, plus fixed cost.
Here, Green coffee beans cost $0.58 for each ounce.
Amina and her mother buy 12.5 ounces of green coffee beans
Total cost = cost each ounce X Number of ounces
TC = 12.5 X 0.58
TC = $ 7.25
Thus, the total cost of the Green coffee beans is $7.25.
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Solve for d -6 = d/3
21
-21
18
-18
Part D What is the y-intercept of the correct graph? What is the y-intercept of the incorrect graph? Are the y-intercepts the same?
Part F about what is the average change in distance for each increase of 1 iron number? what does this mean in terms of the situation
The y-intercept of the correct graph is 185 and y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.
What is y-intercept?The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis.
In the graph it can be seen that the correct graph is intersect y-axis at the value 185. Thus, the y-intercept of the correct graph is 185.
c=185
For the incorrect graph this value is 195. Thus, the y-intercept of the incorrect graph is 195.
b=195
Here, the values of y-intercepts are not the same-
c≠b
185≠195
The average change in distance for each increase of 1 iron number is,
[tex]r=\dfrac{155-145}{3-4}\\r=-10[/tex]
Thus, the y-intercept of the correct graph is 185 and y-intercept of the incorrect graph is 195. The value of average change in distance is -10 for each increase of 1 iron number.
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Drag each expression to its equivalent.
Answer:
x-3+2x+3+2x = 5x
x+8+4x-3x-4 = 2x+4
4x+x-11-5X+25+4x = 4x+14
3x+5-2x-5x+9+8x = 4x+14
5+9x-7-4X-3x+6 = 2x+4
6x-9-5x+4-x+5x+5 = 5x
Step-by-step explanation:
Simplified by adding like terms
f(x)
=
2x + 7 - x2
4
f(2)
=
Be sure to simplify your answer.
Enter
Answer:
[tex]f(2)=\frac{7}{4}[/tex]
Step-by-step explanation:
Step 1: Input 2 for x and solve
[tex]f(x) = \frac{2x + 7 - x^2}{4}[/tex]
[tex]f(2) = \frac{2(2) + 7 - (2)^2}{4}[/tex]
[tex]f(2)=\frac{4+7-4}{4}[/tex]
[tex]f(2)=\frac{7}{4}[/tex]
Answer: [tex]f(2)=\frac{7}{4}[/tex]
In the rectangular prism shown above, the distance between any two neighboring points on a line segment is the same. For example, the distance between points 1 and 2 is the same as the distance between points 13 and 20, which is the same as the distance between points 15 and 16. Place the cross sections indicated by the tiles in order from least area to greatest area.
A rectangular prism is a shape that has six faces which are rectangular.
What is a rectangular prism?Your information is incomplete as the diagram of the rectangular prism isn't given. Therefore, an overview will be given.
It should be noted that a rectangular prism simply means a three dimensional sold shape that has six faces that are rectangles.
The formula that's used to calculate the volume of a rectangular prism will be:
= Length × Width × Height
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Hello, please choose the correct answer.
A.) 5
B.) square root of 5
C.) 25
D.) 7
Answer:
A) 5
Explanation:
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 - (y_2 - y_1)^2}[/tex]
Here given points:
(6, 8), (3, 4)Distance:
[tex]\rightarrow \sf \sqrt{(6 - 3)^2 - (8 - 4)^2}[/tex]
[tex]\rightarrow \sf \sqrt{9 +16}[/tex]
[tex]\rightarrow \sf \sqrt{25}[/tex]
[tex]\rightarrow \sf 5[/tex]
PLEASE HELP ILL MARK BRAINEST!! WHAT IS THE RISE, RUN, AND F(X).
Answer:
First question (on left) f(x) = 5x-3. second question (on right) f)x) = 1/2*x
Step-by-step explanation:
rise(left) 4. run (left) 20.
rise(right) 8. run(right) 4.
Travis is cutting strips of paper for a project. He needs strips that are 114 inches wide. He cut his first strip too wide. His percent error was 10%. How wide did Travis cut the strip of paper? Enter your answer as a mixed number in simplest form in the box.
Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We have:
The length Travis needs to cut = 114 inches
Percent of error = 10%
Let's assume he cuts x inches wide strip
So from the percent of error formula:
[tex]\rm \dfrac{x-114}{114} = \dfrac{10}{100}[/tex]
[tex]\rm x = \dfrac{114}{10}+114[/tex]
[tex]\rm x = \dfrac{1254}{10}\Rightarrow \dfrac {627}{5}[/tex] or
[tex]\rm x = 125\dfrac{2}{5} \ inches[/tex]
Thus, Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches
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Answer:
it’s 1 3/8 I don’t know what dude it’s talking about
Step-by-step explanation:
1. As shown in the diagram below, the radius of a cone is 2.5 cm and its
slant height is 6.5 cm. How many cubic centimeters are in the volume of
the cone?
6.5
The number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
Calculating the volume of a coneFrom the question, we are to determine the volume of the cone
The volume of a cone can be calculated by using the formula,
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
Where V is the volume
r is the radius
and h is the height
From the given information,
radius, r = 2.5 cm
slant height, l = 6.5 cm
First, we will determine the height of the cone
By Pythagoras' theorem
[tex]l^{2} = r^{2} + h^{2}[/tex]
Where [tex]l[/tex] is the slant height
r is the radius
and h is the height of the cone
Then, we can write that
[tex]6.5^{2} = 2.5^{2} + h^{2}[/tex]
[tex]42.25 = 6.25 + h^{2}[/tex]
[tex]h^{2}=42.25 - 6.25[/tex]
[tex]h^{2} =36[/tex]
[tex]h = \sqrt{36}[/tex]
∴ h = 6 cm
Now, putting the parameters into the equation for the determining the volume of a cone, we get
[tex]V = \frac{1}{3}\times \pi \times 2.5^{2} \times 6[/tex]
[tex]V = \pi \times 6.25\times 2[/tex]
[tex]V = 12.5 \pi[/tex] cm³ OR 39.27 cm³
Hence, the number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
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Which of the follow box-and-whisker plots correctly displays this data set?
24, 32, 25, 27, 37, 29, 30, 30, 28, 31, 27, 23
Answer:
Since there isn't any of the following attached, I made my wn attached below
Step-by-step explanation:
Population size: 12
Median: 28.5
Minimum: 23
Maximum: 37
First quartile: 25.5
Third quartile: 30.75
Interquartile Range: 5.25
Outliers: none
Hope this helps you a little more for your last day of finishing hmw :)
Let me know if you need anymore help !
OR have questions
−5 2/3 − 1/6 = i need more letters
Answer:
-5 5/6
Step-by-step explanation:
convert 2/3 into 4/6 and when u subtract a positive from a negative u add it instead
Iggy is practicing for a marathon by running laps on the
track at school. Each lap covers 0.7 kilometers, and he
has already run 19.6 kilometers. How many laps does he
need to run if he wants to complete 91 kilometers?
Find the volume of the solid (pls help me :// )
=====================================================
Explanation:
The triangular face has area of base*height/2 = 4*10/2 = 40/2 = 20 square cm.
Multiply this prism base area by the depth of the prism to get 20*2 = 40 cubic cm.
It might help to place the triangular prism so the triangular face is along the ground, so you can think of that face as the floor of this triangular room. The volume of this room is equal to the floor area times the height of the room.
volume of the room = (floor area)*(height of the room)
volume of the prism = (base area)*(height of the prism)
For any prism, the base faces are always parallel and congruent to each other.