If a diameter is 12.5 cm, what is the radius?

What is the length x of the right triangle, rounded to the nearest<br> tenth?

Zarrin [17]

Answer:

109.5; B

Step-by-step explanation:

From your identity,

CosA = adjacent/ hypothenus

A represent an arbitrary angle between the sides in question.

In the question above, A=64

Hypothenus is the longest side and adjacent is the side just below the angle .

In the above case,

Hypothenus= X

adjacent =48

This means;

Cos64 = 48 /X

X = 48 / cos64; [ from cross multiplication and diving through by cos64]

X = 48 /0.4383 [ cos64 in radian = 0.4383]

= 109.51

= 109.5 to the nearest tenth.

Note( do your calculation of angle in radian or else, you won't get the answer)

6 0

3 years ago

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral a

earnstyle [38]

Given that the figures are similar polygons, the ratio of their ratios should be equal to the square of the ratio of their circumference. If we let x be the lateral area of the smaller cylinder then,
(x/210π) = (24π/60π)²
The value of x from the equation is,
x = 33.6π
Thus, the area of the smaller cylinder is equal to 33.6π mm².

6 0

3 years ago

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Which logarithmic equation is equivalent to the exponential equation below?

aleksandr82 [10.1K]

Option B: $\ln 6=5 x$ is the correct answer.

Explanation:

The exponential equation is $e^{5 x}=6$

If $f(x)=g(x)$ , then $\ln (f(x))=\ln (g(x))$

Thus, the equation becomes

$\ln \left(e^{5 x}\right)=\ln (6)$

Applying log rule, $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$ and thus the equation becomes

$5 x \ln (e)=\ln (6)$

Since, we know that, $\ln (e)=1$ , using this we get,

$5 x=\ln (6)$

Hence, the logarithmic equation which is equivalent to the exponential equation $e^{5 x}=6$ is $\ln 6=5 x$

Thus, Option B is the correct answer.

7 0

3 years ago

I need help with this (don't answer if you don't know)

SashulF [63]

Answer:

Step-by-step explanation:

Here's a step by step tutorial on your calculator on how to do this.

Hit "stat" then "1: Edit". If there are numbers there, arrow up to highlight L1, or L2, or wherever there are numbers. Hit "clear" then "enter" and the numbers will be gone. In L1, enter the Practice throws values. Press 3 then enter, then 12 then enter, then 6 then enter, etc. til all of them are in L1's column. Then arrow over to L2 and do the same with entering all the Free Throw values.

When you're done, hit "stat" again, then arrow over once to "calc" and #4 should say LinReg. That's a linear regression equation. If you have a TI 83, just hit enter and you'll get the equation in the form y = mx + b. If you have a TI 84 or 84+, you'll need to arrow down to the word "calculate" and then you'll see the equation.

One thing...if you have not turned your diagnostics on, you wont be able to see the coefficient of determination (the r-squared value). To make sure it's on:

Hit 2nd, then 0. You have opened up the catalog which lists every single thing your calculator can do in alphabetical order. The hit the button UNDER the MATH button (x to the negative 1) and scroll down until you see "diagnosticsON" and hit enter twice.

If you need to recall the linear regression equation, hit "stat", then "calc" then either enter or calculate and you'll get the linear equation again and an r value and an r-squared value. The closer that number is to 1, the better the data fits that model. I got that the equation is

y = 2.352x - .852 with an r-squared value of .844

To get the quadratic regression equation, hit "stat" then "calc" then choose #5, QuadReg. Repeat the process to calculate your equation. Mine was

$y=.073x^2+1.205x+2.555; r^2=.855$

And for the exponential regression, choose ExpReg (mine is under 0. Yours may be some other number. Just arrow down til you find it, it's there!) My ExpReg equation was

$y=4.229(1.170)^x; r^2=.833$

It appears that the r-squared value is the highest in the quadratic regression equation, so that's the best fit.

4 0

3 years ago

Let y=3t+6 be a linear function representing the distance, in feet, from home for an ant t minutes after starting out from a loc

Marysya12 [62]

Answer:

The y, in the equation, represents the total distance, in feet, from an ant t minutes after starting out from a location near its home. The 6 represents the the distance of the location where the ant starts traveling. The 3 represents the amount of feet covered in one minute. That's why when you increase the minute by one (experiment!!), the distance away from home increases by three, and that means that the ant is traveling at 3 ft/minute. (lol crazy)

3 = the ant's speed in ft/minute

6 0

3 years ago

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